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Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case

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  • Peter J. Hammond
  • Yeneng Sun

Abstract

Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo -algebra, which represents macroeconomic risk, individual agents' random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Peter J. Hammond & Yeneng Sun, 2003. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 743-766, March.
    • Handle: RePEc:spr:joecth:v:21:y:2003:i:2:p:743-766
    DOI: 10.1007/s00199-002-0302-y
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    Cited by:

    1. YiLi Chien & Hanno Lustig, 2010. "The Market Price of Aggregate Risk and the Wealth Distribution," The Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1596-1650, April.
    2. Hammond, Peter J. & Sun, Yeneng, 2016. "The One-way Fubini Property and Conditional Independence : An Equivalence Result," CRETA Online Discussion Paper Series 22, Centre for Research in Economic Theory and its Applications CRETA.
    3. Hellwig, Martin, 2022. "Incomplete-information games in large populations with anonymity," Theoretical Economics, Econometric Society, vol. 17(1), January.
    4. Krueger, Dirk & Lustig, Hanno, 2006. "The Irrelevance of Market Incompleteness for the Price of Aggregate Risk," CEPR Discussion Papers 5936, C.E.P.R. Discussion Papers.
    5. Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 303-325, August.
    6. Peter J. Hammond & Lei Qiao & Yeneng Sun, 2021. "Monte Carlo sampling processes and incentive compatible allocations in large economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1161-1187, April.
    7. Lei Qiao & Yeneng Sun & Zhixiang Zhang, 2016. "Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 43-64, June.
    8. Hammond, Peter J., 2023. "The Monte Carlo Integral of a Continuum of Independent Random Variables," The Warwick Economics Research Paper Series (TWERPS) 1479, University of Warwick, Department of Economics.
    9. Sun, Yeneng & Yannelis, Nicholas C., 2007. "Core, equilibria and incentives in large asymmetric information economies," Games and Economic Behavior, Elsevier, vol. 61(1), pages 131-155, October.
    10. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    11. Laura Veldkamp & Stijn Van Nieuwerburgh, 2005. "Information Acquisition and Portfolio Underdiversification," 2005 Meeting Papers 77, Society for Economic Dynamics.
    12. Krueger, Dirk & Lustig, Hanno, 2010. "When is market incompleteness irrelevant for the price of aggregate risk (and when is it not)?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 1-41, January.
    13. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.

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